The balance of a savings account earning compound interest, the size of a bacteria population in a petri dish, and the amount of a medication remaining in a patient’s bloodstream all share a common feature: at each moment, the quantity changes by a constant percentage rather than a constant amount. Functions that describe this kind of change are called exponential functions, and they are used throughout the sciences, medicine, and finance to model growth and decay.
This chapter introduces exponential functions algebraically, graphically, and numerically, and shows how to recognize an exponential pattern in real data and build a model from it. It also covers the doubling time and half-life of a growing or decaying quantity, and concludes with the natural base \(e\text{,}\) which is the base most commonly used to describe exponential processes in the sciences.
